Some New Properties of Balancing Numbers and Square Triangular Numbers

A number N is a square if it can be written as N = n2 for some
natural number n;
it is a triangular number if it can be written as N
= n(n+1)/2 for some
natural number n; and it is a balancing number if 8N2 +1 is a square.
In this paper, we study some
properties of balancing numbers and square triangular numbers.